Problem: Let’s play a card game called Gap.

You have 28 cards labeled with two-digit numbers. The first digit (from 1 to 4) represents the suit of the card, and the second digit (from 1 to 7) represents the value of the card.

First, you shuffle the cards and lay them face up on the table in four rows of seven cards, leaving a space of one card at the extreme left of each row. The following shows an example of initial layout.

<image>

Next, you remove all cards of value 1, and put them in the open space at the left end of the rows: “11” to the top row, “21” to the next, and so on.

Now you have 28 cards and four spaces, called gaps, in four rows and eight columns. You start moving cards from this layout.

<image>

At each move, you choose one of the four gaps and fill it with the successor of the left neighbor of the gap. The successor of a card is the next card in the same suit, when it exists. For instance the successor of “42” is “43”, and “27” has no successor.

In the above layout, you can move “43” to the gap at the right of “42”, or “36” to the gap at the right of “35”. If you move “43”, a new gap is generated to the right of “16”. You cannot move any card to the right of a card of value 7, nor to the right of a gap.

The goal of the game is, by choosing clever moves, to make four ascending sequences of the same suit, as follows.

<image>

Your task is to find the minimum number of moves to reach the goal layout.



Input

The input starts with a line containing the number of initial layouts that follow.

Each layout consists of five lines - a blank line and four lines which represent initial layouts of four rows. Each row has seven two-digit numbers which correspond to the cards.

Output

For each initial layout, produce a line with the minimum number of moves to reach the goal layout. Note that this number should not include the initial four moves of the cards of value 1. If there is no move sequence from the initial layout to the goal layout, produce “-1”.

Example

Input

4

12 13 14 15 16 17 21
22 23 24 25 26 27 31
32 33 34 35 36 37 41
42 43 44 45 46 47 11

26 31 13 44 21 24 42
17 45 23 25 41 36 11
46 34 14 12 37 32 47
16 43 27 35 22 33 15

17 12 16 13 15 14 11
27 22 26 23 25 24 21
37 32 36 33 35 34 31
47 42 46 43 45 44 41

27 14 22 35 32 46 33
13 17 36 24 44 21 15
43 16 45 47 23 11 26
25 37 41 34 42 12 31


Output

0
33
60
-1

Solution (in CPP):

Solution:
#include <iostream>
#include <cstring>
#include <climits>
#include <queue>
#include <unordered_set>
 
using namespace std;
 
class State
{
public:
    /**
     * 表格数字
     */
    int table[4][8];
    /**
     * 移动回数
     */
    int turn;
 
 
    State(int card[4][7])
    {
        for (int i = 0; i < 4; i++)
            table[i][0] = (10 * (i + 1) + 1);// 11 21 31 41
        for (int i = 0; i < 4; i++)
        {
            memcpy(table[i] + 1, card[i], 7 * sizeof(int));
        }
        // 从这种布局开始游戏
        for (int i = 0; i < 4; i++)
        {
            for (int j = 1; j < 8; j++)
            {
                if (table[i][j] == 11 || table[i][j] == 21 || table[i][j] == 31 || table[i][j] == 41)
                    table[i][j] = 0;
            }
        }
        turn = 0;
    }
 
    State(const State &t)
    {
        memcpy(table, t.table, sizeof(table));
        turn = t.turn;
    }
 
    /**
     * 可以填充空白
     * @param x
     * @param y
     * @return
     */
    bool can_fill_gap(int x, int y)
    {
        if (table[x][y] != 0)
            return false;
        else if (table[x][y - 1] == 0 || (table[x][y - 1]) % 10 == 7) // x7 has no successor
            return false;
        else
            return true;
    }
 
    /**
     * 填充空白
     * @param x
     * @param y
     */
    void fill_gap(int x, int y)
    {
        int s, sx, sy;
        sx = sy = -1;
 
        s = table[x][y - 1] + 1;
 
        for (int i = 0; i < 4; i++)
        {
            for (int j = 0; j < 8; j++)
            {
                if (table[i][j] == s)
                {
                    sx = i;
                    sy = j;
                }
            }
        }
 
        table[x][y] = table[sx][sy];
        table[sx][sy] = 0;
 
        turn++;
    }
 
    /**
     * 是否是游戏结束状态，即每行都是升序，最后一列全为0
     * @return
     */
    bool done()
    {
        for (int i = 0; i < 4; i++)
        {
            for (int j = 0; j < 7; j++)
            {
                if (table[i][j] != (10 * (i + 1) + (j + 1)))
                    return false;
            }
            if (table[i][7] != 0)
                return false;
        }
 
        return true;
    }
 
    bool operator==(const State &s) const
    {
        int i, j;
        for (i = 0; i < 4; i++)
        {
            for (j = 1; j < 8; j++)
            {
                if (table[i][j] != s.table[i][j])
                    return false;
            }
        }
        return true;
    }
 
};
 
struct StateHash
{
    size_t operator()(const State &s) const
    {
        size_t hash = 0;
        for (int i = 0; i < 4; i++)
        {
            for (int j = 1; j < 8; j++)
            {
                hash += s.table[i][j];
                hash <<= 1;
            }
        }
 
        return hash;
    }
};
 
int solve(int card[4][7])
{
    queue<State> que;
    unordered_set<State, StateHash> visited;
    //准备BFS
    bool end = false;
    int ans = INT_MAX;
    State init(card);
    if (init.done())
        return 0;
    que.push(init);
    visited.insert(init);
    //BFS
    while (!que.empty() && !end)
    {
        State s = que.front();
        que.pop();
        for (int i = 0; i < 4; i++)
        {
            for (int j = 1; j < 8; j++)
            {
                if (s.can_fill_gap(i, j))
                {
                    State temp(s);
                    temp.fill_gap(i, j);
                    // 结束
                    if (temp.done())
                    {
                        end = true;
                        ans = temp.turn;
                    }// 未遍历
                    else if (visited.find(temp) == visited.end())
                    {
                        que.push(temp);
                        visited.insert(temp);
                    }
                }
            }
        }
    }
 
    if (ans == INT_MAX)
        ans = -1;
    return ans;
}
 
int main()
{
    int n;
    scanf("%d", &n);
    while (n--)
    {
        int card[4][7];
        for (int i = 0; i < 4; ++i)
        {
            for (int j = 0; j < 7; ++j)
            {
                scanf("%d", &card[i][j]);
            }
        }
 
        printf("%d\n", solve(card));
    }
    return 0;
}